A cluster calculation investigation of A- and B-sites-ordered perovskite oxide CaCu₃Fe₂Os₂O₁₂

Taking the quadruple perovskite oxide CaCu₃Fe₂Os₂O₁₂ as an example, by performing both experimental sum rules and theoretical configuration interaction cluster calculations, we have investigated the spin and orbital configurations of all the transition metal cations, Cu, Fe, and Os, as well as their local microscopic physical parameters of crystal field, spin–orbit coupling (SOC), Coulomb potential, and hybridization. Specifically, we found that Os⁵⁺ (5d³) with a half-filled t_2g orbital exhibits a large orbital moment on account of the mixing of t_2g and e_g orbitals, which can be ascribed to the strong SOC of the 5d elements. On the other hand, SOC of the Cu²⁺ (3d⁹) is markedly reduced, but is still nonnegligible compared to the crystal field 10Dq, leading to a finite orbital moment of Cu²⁺. This work provides a microscopic and element-selective perspective of the local environment of magnetic cations in complex compounds.